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A144115
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Total number of Fibonacci parts in all partitions of n.
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6
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1, 3, 6, 11, 19, 32, 49, 77, 114, 169, 241, 345, 480, 667, 910, 1237, 1656, 2213, 2918, 3840, 5003, 6497, 8368, 10751, 13711, 17441, 22052, 27806, 34879, 43645, 54355, 67535, 83571, 103171, 126907, 155766, 190554, 232629, 283158, 343969, 416716
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..1000
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EXAMPLE
| Contribution from Omar E. Pol, Nov 20 2011 (Start):
For n = 6 we have:
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. Number of
Partitions Fibonacci parts
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6 .......................... 0
3 + 3 ...................... 2
4 + 2 ...................... 1
2 + 2 + 2 .................. 3
5 + 1 ...................... 2
3 + 2 + 1 .................. 3
4 + 1 + 1 .................. 2
2 + 2 + 1 + 1 .............. 4
3 + 1 + 1 + 1 .............. 4
2 + 1 + 1 + 1 + 1 .......... 5
1 + 1 + 1 + 1 + 1 + 1 ...... 6
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Total ..................... 32
So a(6) = 32. (End)
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MAPLE
| b:= proc(n) option remember; false end: l:= [0, 1]: for k to 100 do b(l[1]):= true; l:= [l[2], l[1]+l[2]] od: aa:= proc(n, i) option remember; local g, h; if n=0 then [1, 0] elif i=0 or n<0 then [0, 0] else g:= aa(n, i-1); h:= aa(n-i, i); [g[1]+h[1], g[2]+h[2] +`if`(b(i), h[1], 0)] fi end: a:= n-> aa(n, n)[2]: seq (a(n), n=1..60); # Alois P. Heinz, Jun 24 2009
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CROSSREFS
| Cf. A000045, A006128, A037032, A144116, A144117, A144118.
Sequence in context: A050228 A114089 A001976 * A183088 A116557 A001911
Adjacent sequences: A144112 A144113 A144114 * A144116 A144117 A144118
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KEYWORD
| nonn
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AUTHOR
| Omar E. Pol (info(AT)polprimos.com), Sep 11 2008
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jun 24 2009
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