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A136530
a(n) = 2^n*(3*n^2 + 13*n + 8)/8.
1
1, 6, 23, 74, 216, 592, 1552, 3936, 9728, 23552, 56064, 131584, 305152, 700416, 1593344, 3596288, 8060928, 17956864, 39780352, 87687168, 192413696, 420478976, 915406848, 1986002944, 4294967296, 9261023232, 19914555392, 42714791936
OFFSET
0,2
COMMENTS
Matrix-vector product A007318 * A000326.
Double binomial transform of [1, 4, 3, 0, 0, 0, ...].
FORMULA
Binomial transform of the pentagonal numbers (A000326 starting 1, 5, 12, 22, ...).
From Colin Barker, Aug 12 2012: (Start)
a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3).
G.f.: (1+x)*(1-x)/(1-2*x)^3. (End)
E.g.f.: (1/2)*(2 + 8*x + 3*x^2)*exp(2*x). - G. C. Greubel, Oct 03 2022
EXAMPLE
a(3) = 23 = (1, 2, 1) dot (1, 5, 12) = (1 + 10 + 12).
MATHEMATICA
Table[2^n(3n^2+13n+8)/8, {n, 0, 30}] (* or *) LinearRecurrence[{6, -12, 8}, {1, 6, 23}, 30] (* Harvey P. Dale, May 22 2021 *)
PROG
(Magma) [2^(n-3)*(3*n^2+13*n+8): n in [0..30]]; // G. C. Greubel, Oct 03 2022
(SageMath) [2^(n-3)*(3*n^2+13*n+8) for n in range(31)] # G. C. Greubel, Oct 03 2022
CROSSREFS
Sequence in context: A045618 A038737 A038797 * A259033 A374856 A054459
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jan 03 2008
EXTENSIONS
More terms from Carl Najafi, Sep 08 2011
STATUS
approved