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URL: https://oeis.org/A202462

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A202462
a(n) = Sum_{j=1..n} Sum_{i=1..n} F(i,j), where F is the Fibonacci fusion array of A202453.
5
1, 5, 21, 70, 214, 614, 1703, 4619, 12363, 32812, 86636, 228012, 598893, 1571089, 4118305, 10790194, 28262594, 74014290, 193807315, 507451415, 1328617751, 3478516440, 9107117016, 23843134680, 62422772569, 163425968669, 427856404653
OFFSET
1,2
COMMENTS
Partial sums of A188516.
FORMULA
G.f.: x*(1+2*x^2-x^3)/((1+x)*(1-3*x+x^2)*(1-x-x^2)*(1-x)^2). - R. J. Mathar, Dec 20 2011
a(n) = Fibonacci(n+2)*Fibonacci(n+3) - 2*Fibonacci(n+4) + n + 4. - G. C. Greubel, Jul 23 2019
MATHEMATICA
(* First program *)
n = 28;
Q = NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[
Table[Fibonacci[k], {k, 1, n}]];
P = Transpose[Q]; F = P.Q;
a[m_] := Sum[F[[i]][[j]], {i, 1, m}, {j, 1, m}]
Table[a[m], {m, 1, n}] (* A202462 *)
Table[a[m] - a[m - 1], {m, 1, n}] (* A188516 *)
(* Additional programs *)
LinearRecurrence[{5, -6, -4, 10, -2, -3, 1}, {1, 5, 21, 70, 214, 614, 1703}, 30] (* Harvey P. Dale, Jul 23 2015 *)
With[{F=Fibonacci}, Table[F[n+2]*F[n+3] -2*F[n+4] +n+4, {n, 30}]] (* G. C. Greubel, Jul 23 2019 *)
PROG
(PARI) vector(30, n, f=fibonacci; f(n+2)*f(n+3) -2*f(n+4) +n+4) \\ G. C. Greubel, Jul 23 2019
(Magma) F:=Fibonacci; [F(n+2)*F(n+3) -2*F(n+4) +n+4: n in [1..30]]; // G. C. Greubel, Jul 23 2019
(SageMath) f=fibonacci; [f(n+2)*f(n+3)-2*f(n+4) +n+4 for n in (1..30)] # G. C. Greubel, Jul 23 2019
(GAP) F:=Fibonacci;; List([1..30], n-> F(n+2)*F(n+3) -2*F(n+4) +n+4); # G. C. Greubel, Jul 23 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Dec 19 2011
STATUS
approved