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A274772 Zero together with the partial sums of A056640. 1
0, 1, 6, 24, 66, 149, 292, 520, 860, 1345, 2010, 2896, 4046, 5509, 7336, 9584, 12312, 15585, 19470, 24040, 29370, 35541, 42636, 50744, 59956, 70369, 82082, 95200, 109830, 126085, 144080, 163936, 185776, 209729, 235926, 264504, 295602, 329365, 365940, 405480, 448140, 494081, 543466, 596464, 653246, 713989, 778872, 848080, 921800, 1000225, 1083550 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
I
LINKS
FORMULA
a(n) = (4*n^4+8*n^3+2*n^2+4*n+3*(1-(-1)^n))/24. Therefore :
a(2*k) = k*(k+1)*(8*k^2+1)/3, a(2*k+1) = (k+1)*(8*k^3+16*k^2+9*k+3)/3.
From Colin Barker, Nov 11 2016: (Start)
G.f.: x*(1 + 2*x + 5*x^2) / ((1 - x)^5 * (1 + x)).
a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6) for n>5.
(End)
EXAMPLE
a(0) = 0, a(1) = 1, a(2) = 6, a(3) = 24, a(4) = 66.
MATHEMATICA
LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 1, 6, 24, 66, 149}, 60] (* Harvey P. Dale, Jun 19 2021 *)
PROG
(PARI) concat(0, Vec(x*(1 + 2*x + 5*x^2) / ((1 - x)^5 * (1 + x)) + O(x^50))) \\ Colin Barker, Nov 11 2016
CROSSREFS
Sequence in context: A101877 A270851 A092348 * A369177 A234271 A338512
KEYWORD
nonn,easy
AUTHOR
Luce ETIENNE, Nov 11 2016
STATUS
approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)