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A015226 Even hexagonal pyramidal numbers. 2
22, 50, 252, 372, 946, 1222, 2360, 2856, 4750, 5530, 8372, 9500, 13482, 15022, 20336, 22352, 29190, 31746, 40300, 43460, 53922, 57750, 70312, 74872, 89726, 95082, 112420, 118636, 138650, 145790, 168672, 176800, 202742, 211922, 241116 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Ivan Panchenko, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1, 3, -3, -3, 3, 1, -1).

FORMULA

Even numbers of form n(n+1)(4n-1)/6.

Contribution from Ant King, Oct 25 2012: (Start)

a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7).

a(n) = 3*a(n-2) -3*a(n-4) +a(n-6) +256.

a(n) = (4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9)/24.

G. f. 2*x*(11 + 14*x + 68*x^2 + 18*x^3 + 17*x^4) / ((1-x)^4*(1+x)^3).

(End)

E.g.f.: (1/6)*(3*(15 - 30*x + 8*x^2)*exp(-x) + (87 + 348*x + 228*x^2 + 32*x^3 ) *exp(x)). - G. C. Greubel, Jul 30 2016

MATHEMATICA

Select[ Table[ n(n+1)(4n-1)/6, {n, 100} ], EvenQ ]

LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {22, 50, 252, 372, 946, 1222, 2360}, 35] (* Ant King, Oct 25 2012 *)

PROG

(PARI) a(n)=(4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9)/24 \\ Charles R Greathouse IV, Jul 30 2016

CROSSREFS

Sequence in context: A039345 A043168 A043948 * A092221 A191279 A200880

Adjacent sequences:  A015223 A015224 A015225 * A015227 A015228 A015229

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian, Dec 11 1999

EXTENSIONS

More terms from Erich Friedman.

STATUS

approved

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Last modified October 13 18:14 EDT 2019. Contains 327981 sequences. (Running on oeis4.)