A276915 Indices of triangular numbers in A276914 which are also pentagonal.

0, 1, 10, 143, 1988, 27693, 385710, 5372251, 74825800, 1042188953, 14515819538, 202179284583, 2815994164620, 39221739020101, 546288352116790, 7608815190614963, 105977124316492688, 1476070925240282673, 20559015829047464730, 286350150681424223551

Offset

0,3

Comments

A276914(a(n)) = A014979(n + 1). All numbers which are both triangular and pentagonal can be found in sequence A276914.

Links

Daniel Poveda Parrilla, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (13,13,-1).

Formula

a(n) = 14*a(n-1) - a(n-2) - 4*(-1)^n for n>1, a(0)=0, a(1)=1.

a(n) = (A046175(n) + (A046175(n) mod 2))/2.

From Colin Barker, Sep 23 2016: (Start)

G.f.: x*(1 - 3*x) / ((1 + x)*(1 - 14*x + x^2)).

a(n) = 13*a(n-1) + 13*a(n-2) - a(n-3) for n>2.

a(n) = ( -6*(-1)^n + (3+sqrt(3))*(7-4*sqrt(3))^n - (-3+sqrt(3))*(7+4*sqrt(3))^n )/24. (End)

Mathematica

RecurrenceTable[{a[n] == 14 a[n - 1] - a[n - 2] - 4 (-1)^n, a[0] == 0, a[1] == 1}, a, {n, 19}] (* Michael De Vlieger, Sep 23 2016 *)

Prog

(PARI) concat(0, Vec(x*(1-3*x)/((1+x)*(1-14*x+x^2)) + O(x^30))) \\ Colin Barker, Sep 23 2016

Crossrefs

Cf. A014979, A046175, A276914.

Sequence in context: A263055 A159327 A356468 * A284219 A180914 A268737

Adjacent sequences: A276912 A276913 A276914 * A276916 A276917 A276918

Keyword

nonn,easy

Author

Daniel Poveda Parrilla, Sep 22 2016

Status

approved