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Search: id:A001891
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| A001891 |
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Hit polynomials; convolution of natural numbers with Fibonacci numbers F(2), F(3), F(4),....
(Formerly M3384 N1365)
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+0
13
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| 0, 1, 4, 10, 21, 40, 72, 125, 212, 354, 585, 960, 1568, 2553, 4148, 6730, 10909, 17672, 28616, 46325, 74980, 121346, 196369, 317760, 514176, 831985, 1346212, 2178250, 3524517, 5702824, 9227400, 14930285
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = sum of the n-th row of the triangle in A119457 for n>0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2006
Convolution of odds (A005408) with Fibonacci numbers (A000045) - Graeme McRae (g_m(AT)mcraefamily.com), Jun 06 2006
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
J. Riordan, ``The enumeration of permutations with three-ply staircase restrictions,'' unpublished memorandum, Bell Telephone Laboratories, Murray Hill, NJ, Oct 1963.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: x ( 1 + x ) / (( 1 - x - x^2 )*( 1 - x )^2). a(n)=F(n+5)-(5+2*n) - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
a(n)=a(n-1)+a(n-2)+(2n+1); a(-x)=0 - Barry E. Williams, Mar 27 2000
a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) - Sam Lachterman (slachterman(AT)fuse.net), Sep 22 2003
a(n) - a(n-1) = A101220(2,1,n). - Ross La Haye (rlahaye(AT)new.rr.com), May 31 2006
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MAPLE
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A001891:=-z*(1+z)/(z**2+z-1)/(-1+z)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Partial sums of A001911.
Right-hand column 5 of triangle A011794.
Sequence in context: A023538 A085360 A024988 this_sequence A121497 A132925 A053643
Adjacent sequences: A001888 A001889 A001890 this_sequence A001892 A001893 A001894
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KEYWORD
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nonn
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AUTHOR
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njas, Simon Plouffe (plouffe(AT)math.uqam.ca)
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