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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 G. C. Greubel, Table of n, a(n) for n = 0..1000 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:=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 Cf. A003269, A079977, A099573, A099577, A103609. Sequence in context: A326632 A240206 A229816 * A144118 A187069 A038000 Adjacent sequences: A099571 A099572 A099573 * A099575 A099576 A099577 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.)