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 A199936 Total sum of Fibonacci parts in all partitions of n. 4
 0, 1, 4, 9, 16, 31, 52, 80, 133, 197, 298, 428, 621, 879, 1230, 1696, 2329, 3142, 4231, 5619, 7447, 9781, 12771, 16553, 21391, 27440, 35089, 44600, 56510, 71232, 89538, 112011, 139759, 173679, 215279, 265840, 327527, 402162, 492703, 601830, 733550, 891634 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..5000 FORMULA G.f.: Sum_{i>=2} Fibonacci(i)*x^Fibonacci(i)/(1 - x^Fibonacci(i)) / Product_{j>=1} (1 - x^j). - Ilya Gutkovskiy, Feb 01 2017 EXAMPLE For n = 6 we have: -------------------------------------- .                         Sum of Partitions            Fibonacci parts -------------------------------------- 6 .......................... 0 3 + 3 ...................... 6 4 + 2 ...................... 2 2 + 2 + 2 .................. 6 5 + 1 ...................... 6 3 + 2 + 1 .................. 6 4 + 1 + 1 .................. 2 2 + 2 + 1 + 1 .............. 6 3 + 1 + 1 + 1 .............. 6 2 + 1 + 1 + 1 + 1 .......... 6 1 + 1 + 1 + 1 + 1 + 1 ...... 6 ------------------------------------ Total ..................... 52 So a(6) = 52. MAPLE b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,       `if`(i>n, 0, ((p, m)-> p +`if`(issqr(m+4) or issqr(m-4),       [0, p[1]*i], 0))(b(n-i, i), 5*i^2)) +b(n, i-1)))     end: a:= n-> b(n\$2)[2]: seq(a(n), n=0..50);  # Alois P. Heinz, Feb 01 2017 MATHEMATICA max = 42; F = Fibonacci; gf = Sum[F[i]*x^F[i]/(1-x^F[i]), {i, 2, max}] / Product[1-x^j, {j, 1, max}] + O[x]^max; CoefficientList[gf, x] (* Jean-François Alcover, Feb 21 2017, after Ilya Gutkovskiy *) b[n_, i_] := b[n, i] = If[n==0, {1, 0}, If[i<1, 0, If[i>n, 0, Function[{p, m}, p+If[IntegerQ @ Sqrt[m+4] || IntegerQ @ Sqrt[m-4], {0, p[[1]]*i}, 0] ][b[n-i, i], 5*i^2]]+b[n, i-1]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 21 2017, after Alois P. Heinz *) CROSSREFS Cf. A000045, A066186, A073118, A144115, A194544, A194545. Sequence in context: A073141 A093175 A138992 * A326958 A281904 A007679 Adjacent sequences:  A199933 A199934 A199935 * A199937 A199938 A199939 KEYWORD nonn AUTHOR Omar E. Pol, Nov 21 2011 EXTENSIONS More terms from Alois P. Heinz, Nov 21 2011 STATUS approved

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Last modified April 4 08:58 EDT 2020. Contains 333213 sequences. (Running on oeis4.)