A046196 Indices of square numbers which are also heptagonal.

1, 9, 77, 1519, 12987, 111035, 2190397, 18727245, 160112393, 3158550955, 27004674303, 230881959671, 4554628286713, 38940721617681, 332931625733189, 6567770830889191, 56152493568021699, 480087173425298867, 9470720983513926709, 80971856784365672277

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..950
• Eric Weisstein's World of Mathematics, Heptagonal Square Number.
• Index entries for linear recurrences with constant coefficients, signature (0,0,1442,0,0,-1).

Crossrefs

Cf. A036354, A046195.

Programs

Maple

for n from 1 to 10000 do m:=sqrt((5*n*n-3*n)/2):
if (trunc(m)=m) then print(n,m): end if: end do: # Paul Weisenhorn, May 01 2009

Mathematica

LinearRecurrence[{ 0, 0, 1442, 0, 0, -1 } , {1, 9, 77, 1519, 12987, 111035 }, 17] (* Ant King, Nov 11 2011 *)

PARI

Vec(x*(x+1)*(x^4+8*x^3+69*x^2+8*x+1)/(x^6-1442*x^3+1) + O(x^50)) \\ Colin Barker, Jun 23 2015

Formula

From Paul Weisenhorn, May 01 2009: (Start)

a(n+6) = 1442*a(n+3)-a(n) with

a(-2)=-77; a(-1)=-9; a(0)=-1; a(1)=1; a(2)=9; a(3)=77;

A = (721+sqrt(10)*228)^k; B = (721-sqrt(10)*228)^k;

a(3*k+1) = (7*(A-B)/sqrt(10)+2*(A+B))/4;

a(3*k+2) = (57*(A-B)/sqrt(10)+18*(A+B))/4;

a(3*k) = (7*(A-B)/sqrt(10)-2*(A+B))/4;

(End)

G.f.: x * (1 + x) * (1 + 8*x + 69*x^2 + 8*x^3 + x^4) / (1-1442*x^3 + x^6). - Ant King, Nov 11 2011