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, 692285371147655233025

Offset

1,2

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 38.

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A036354, A046195.

Sequence in context: A046150 A124131 A000445 * A231596 A350428 A190980

Adjacent sequences: A046193 A046194 A046195 * A046197 A046198 A046199

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved