A202462 a(n) = Sum_{j=1..n} Sum_{i=1..n} F(i,j), where F is the Fibonacci fusion array of A202453.

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

Author

Clark Kimberling, Dec 19 2011

Keywords

• nonn

Comments

Partial sums of A188516.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-6,-4,10,-2,-3,1).

Crossrefs

Cf. A000045, A188616, A202451.

Programs

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

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

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 *)

PARI

vector(30, n, f=fibonacci; f(n+2)*f(n+3) -2*f(n+4) +n+4) \\ G. C. Greubel, Jul 23 2019

Sage

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

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