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

1,2

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).

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
(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
(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

Cf. A000045, A188616, A202451.

Sequence in context: A099899 A269566 A271492 * A354701 A055280 A268304

Adjacent sequences: A202459 A202460 A202461 * A202463 A202464 A202465

Keyword

nonn

Author

Clark Kimberling, Dec 19 2011

Status

approved