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A014803 Squares of even hexagonal pyramidal numbers. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 25 07:19 EDT 2022. Contains 356959 sequences. (Running on oeis4.)