

A129895


a(1)=1. a(n) = a(n1) + number of triangular numbers among the first (n1) terms of the sequence.


2



1, 2, 3, 5, 7, 9, 11, 13, 15, 18, 21, 25, 29, 33, 37, 41, 45, 50, 55, 61, 67, 73, 79, 85, 91, 98, 105, 113, 121, 129, 137, 145, 153, 162, 171, 181, 191, 201, 211, 221, 231, 242, 253, 265, 277, 289, 301, 313, 325, 338, 351, 365, 379, 393, 407, 421, 435, 450, 465, 481
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OFFSET

1,2


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2, 0, 2, 0, 2, 0, 2, 1).


FORMULA

For k=1,3: a(8*n+k) = (4*n+k)*(2*n+1).  Reinhard Zumkeller, Dec 20 2007
G.f.: x*(x^7  x^6  x^5 + x^4 + x^3  x^2 + 1) / ((x1)^3*(x+1)*(x^4+1)).  Colin Barker, Mar 29 2013
a(n) = 2*a(n1)  2*a(n3) + 2*a(n5)  2*a(n7) + a(n8); a(1)=1, a(2)=2, a(3)=3, a(4)=5, a(5)=7, a(6)=9, a(7)=11, a(8)=13.  Harvey P. Dale, May 16 2014


MAPLE

T := {seq((1/2)*j*(j+1), j = 1 .. 40)}: a[1] := 1; for n from 2 to 60 do a[n] := a[n1]+nops(`intersect`(T, {seq(a[i], i = 1 .. n1)})) end do: seq(a[n], n = 1 .. 60); # Emeric Deutsch, Jun 21 2007


MATHEMATICA

nxt[{a_, t_}]:=Module[{x=t}, {a+t, If[IntegerQ[(Sqrt[8(a+t)+1]1)/2], x+1, x]}]; Transpose[NestList[nxt, {1, 1}, 70]][[1]] (* or *) LinearRecurrence[ {2, 0, 2, 0, 2, 0, 2, 1}, {1, 2, 3, 5, 7, 9, 11, 13}, 70] (* Harvey P. Dale, May 16 2014 *)


CROSSREFS

Cf. A097602.
Sequence in context: A046654 A280724 A023543 * A256212 A096149 A033055
Adjacent sequences: A129892 A129893 A129894 * A129896 A129897 A129898


KEYWORD

nonn


AUTHOR

Leroy Quet, Jun 04 2007


EXTENSIONS

More terms from Emeric Deutsch, Jun 21 2007


STATUS

approved



