A014803 Squares of even hexagonal pyramidal numbers.

484, 2500, 63504, 138384, 894916, 1493284, 5569600, 8156736, 22562500, 30580900, 70090384, 90250000, 181764324, 225660484, 413552896, 499611904, 852056100, 1007808516, 1624090000, 1888771600, 2907582084, 3335062500, 4943777344, 5605816384, 8050755076

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).

Formula

G.f.: -4*(289*x^10 +936*x^9 +20757*x^8 +19952*x^7 +110626*x^6 +44832*x^5 +99442*x^4 +15696*x^3 +14525*x^2 +504*x +121)/((x -1)^7*(x +1)^6). [Colin Barker, Nov 16 2012]

From Wesley Ivan Hurt, Aug 30 2015: (Start)

a(n) = a(n-1)+6*a(n-2)-6*a(n-3)-15*a(n-4)+15*a(n-5)+20*a(n-6)-20*a(n-7)-15*a(n-8)+15*a(n-9)+6*a(n-10)-6*a(n-11)-a(n-12)+a(n-13), n>12.

a(n) = ((4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9))^2/576.

a(n) = A015226(n)^2. (End)

E.g.f.: (512*x^6+11904*x^5+90408*x^4+269664*x^3+301086*x^2+98928*x+4797)*exp(x)/18 -(256*x^5-4320*x^4+21816*x^3-37452*x^2+18270*x-1305)*exp(-x)/6. - Robert Israel, Aug 31 2015

Maple

A014803:=n->((4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9))^2/576: seq(A014803(n), n=0..40); # Wesley Ivan Hurt, Aug 30 2015

Mathematica

CoefficientList[Series[- 4 (289 x^10 + 936 x^9 + 20757 x^8 + 19952 x^7 + 110626 x^6 + 44832 x^5 + 99442 x^4 + 15696 x^3 + 14525 x^2 + 504 x + 121)/((x - 1)^7 (x + 1)^6), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 15 2013 *)
Table[((4*n + (-1)^n + 5)*(4*n + (-1)^n + 7)*(8*n + 2*(-1)^n + 9))^2/
576, {n, 0, 40}] (* Wesley Ivan Hurt, Aug 30 2015 *)

Prog

(Magma) [((4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9))^2/576 : n in [0..40]]; // Wesley Ivan Hurt, Aug 30 2015

Crossrefs

Cf. A015226.

Sequence in context: A329872 A199330 A281398 * A236647 A237078 A085120

Adjacent sequences: A014800 A014801 A014802 * A014804 A014805 A014806

Keyword

nonn,easy

Author

Mohammad K. Azarian

Extensions

Corrected and extended by James A. Sellers

Status

approved