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Search: id:A036221
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| A036221 |
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Expansion of 1/(1-3*x)^8; 8-fold convolution of A000244 (powers of 3). |
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+0
2
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| 1, 24, 324, 3240, 26730, 192456, 1250964, 7505784, 42220035, 225173520, 1148384952, 5637526128, 26778249108, 123591918960, 556163635320, 2447119995408, 10553204980197, 44695926974952, 186233029062300
(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+8,8) (O. Gerard's triangle).
With a different offset, number of n-permutations (n>=7) of 4 objects: u, v, z, x with repetition allowed, containing exactly seven (7) u's. Example: a(1)=24 because we have uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008
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FORMULA
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a(n) = 3^n*binomial(n+7, 7); G.f. 1/(1-3*x)^8.
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MAPLE
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seq(binomial(n+7, 7)*3^n, n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 23 2008
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PROGRAM
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(Other) SAGE: [lucas_number2(n, 3, 0)*binomial(n, 7)/3^7 for n in xrange(7, 26)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2009]
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CROSSREFS
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A000244, A027465.
Sequence in context: A004413 A069779 A006922 this_sequence A022652 A138453 A004317
Adjacent sequences: A036218 A036219 A036220 this_sequence A036222 A036223 A036224
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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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