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Search: id:A036220
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| A036220 |
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Expansion of 1/(1-3*x)^7; 7-fold convolution of A000244 (powers of 3). |
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+0
4
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| 1, 21, 252, 2268, 17010, 112266, 673596, 3752892, 19702683, 98513415, 472864392, 2192371272, 9865670724, 43257171636, 185387878440, 778629089448, 3211844993973, 13036312034361, 52145248137444, 205836505805700
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n)=A027465(n+7,7) (O. Gerard's triangle).
With a different offset, number of n-permutations (n>=6) of 4 objects: u,v, z, x with repetition allowed, containing exactly six (6) u's. Example: a(1)=21 because we have uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu, uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu, uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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FORMULA
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a(n) = 3^n*binomial(n+6, 6); G.f. 1/(1-3*x)^7.
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MAPLE
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seq(binomial(n+6, 6)*3^n, n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 16 2008
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PROGRAM
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(Other) SAGE: lucas_number2(n, 3, 0)*binomial(n, 6)/729 for n in xrange(6, 26)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2009]
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CROSSREFS
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A000244, A027465.
Sequence in context: A165099 A165108 A023019 this_sequence A022649 A165094 A125433
Adjacent sequences: A036217 A036218 A036219 this_sequence A036221 A036222 A036223
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KEYWORD
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easy,nonn
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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