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A099574 Diagonal sums of triangle A099573. 4
1, 1, 2, 2, 4, 5, 9, 11, 18, 23, 37, 48, 74, 97, 147, 195, 290, 387, 568, 763, 1108, 1495, 2152, 2915, 4167, 5662, 8047, 10962, 15506, 21168, 29825, 40787, 57280, 78448, 109870, 150657, 210521, 288969, 403020, 553677, 770963, 1059932, 1473898 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..floor(k/2)} binomial(n-k-j, j).
G.f.: (1-x)*(1+x)*(1+x^2) / ( (1-x-x^4)*(1-x^2-x^4) ). - R. J. Mathar, Nov 11 2014
From G. C. Greubel, Jul 25 2022: (Start)
a(n) = A003269(n+5) - A079977(n+3) - A079977(n+2).
a(n) = A003269(n+5) - A103609(n+5). (End)
MATHEMATICA
a[n_]:= a[n]= Sum[Binomial[n-k-j, j], {k, 0, Floor[n/2]}, {j, 0, Floor[k/2]}];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Jul 25 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x^4)/((1-x^2-x^4)*(1-x-x^4)) )); // G. C. Greubel, Jul 25 2022
(SageMath)
@CachedFunction
def A099574(n): return sum(sum(binomial(n-k-j, j) for j in (0..(k//2))) for k in (0..(n//2)))
[A099574(n) for n in (0..40)] # G. C. Greubel, Jul 25 2022
CROSSREFS
Sequence in context: A326632 A240206 A229816 * A144118 A187069 A038000
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 23 2004
STATUS
approved

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Last modified February 22 09:46 EST 2024. Contains 370250 sequences. (Running on oeis4.)