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 A106523 Diagonal sums of number triangle A106522. 2
 1, 1, 3, 4, 10, 14, 33, 49, 109, 170, 362, 586, 1207, 2011, 4037, 6878, 13536, 23464, 45475, 79891, 153011, 271612, 515460, 922372, 1738101, 3129565, 5865063, 10611336, 19802382, 35960970, 66888917, 121820229, 226016385, 412547222 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,3,1,0,-1). FORMULA G.f.: (1+x)/((1+x-x^2)*(1-x-x^2-x^3)). a(n) = 3*a(n-2) + a(n-3) - a(n-5). a(n) = Sum_{k=0..floor(n/2)} A106522(n-k, k) a(n) = (1/11)*( 10*T(n+2) + 5*T(n+1) + 3*T(n) + (-1)^n*( F(n+1) + 3*F(n) ) ), where T(n) = A000073, and F(n) = A000045. - G. C. Greubel, Aug 10 2021 MATHEMATICA T[n_]:= T[n]= If[n<2, 0, If[n==2, 1, T[n-1] + T[n-2] + T[n-3]]]; (* A000073 *) a[n_]:= (1/11)*((-1)^n*(Fibonacci[n+2] +2*Fibonacci[n]) +10*T[n+2] +5*T[n+1] + 3*T[n]); Table[a[n], {n, 0, 40}] (* G. C. Greubel, Aug 10 2021 *) PROG (Magma) I:=[1, 1, 3, 4, 10]; [n le 5 select I[n] else 3*Self(n-2) + Self(n-3) -Self(n-5): n in [1..41]]; // G. C. Greubel, Aug 10 2021 (Sage) @CachedFunction def T(n): if (n<2): return 0 elif (n==2): return 2 else: return T(n-1) + T(n-2) + T(n-3) def a(n): return (1/11)*((-1)^n*(fibonacci(n+2) +2*fibonacci(n)) +10*T(n+2) +5*T(n+1) + 3*T(n)) [a(n) for n in (0..40)] # G. C. Greubel, Aug 10 2021 CROSSREFS Cf. A106522, A000045, A000073. Sequence in context: A173285 A025084 A134512 * A007068 A121720 A056515 Adjacent sequences: A106520 A106521 A106522 * A106524 A106525 A106526 KEYWORD easy,nonn AUTHOR Paul Barry, May 06 2005 STATUS approved

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Last modified September 22 11:27 EDT 2023. Contains 365523 sequences. (Running on oeis4.)