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Search: id:A160175
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| A160175 |
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Expansion of 1/(1-2x-2x^2-2x^3-2x^4) |
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+0
1
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| 1, 2, 6, 18, 54, 160, 476, 1416, 4212, 12528, 37264, 110840, 329688, 980640, 2916864, 8676064, 25806512, 76760160, 228319200, 679123872, 2020019488
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OFFSET
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0,2
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COMMENT
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a(n) is the number of ways two opposing baseball teams could score a combined total of n runs (tallying the score just prior to each "batter up!") considering the order of the scoring as important. Equivalently, a(n) is the number of 2-colored tilings of an n-board with tiles of length at most 4.
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REFERENCES
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Arthur Benjamin and Jennifer Quinn, Proofs that Really Count, Mathematical Association of America,2003,p.36
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FORMULA
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a(n)=2(a(n-1)+a(n-2)+a(n-3)+a(n-4))
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MATHEMATICA
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RecurrenceTable[{a[n] == 2(a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4]), a[0] == 1, a[1] == 2, a[2] == 6, a[3] == 18}, a, {n, 0, 20}]
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CROSSREFS
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Cf. A077835, A002605, A000079
Sequence in context: A120010 A132790 A072850 this_sequence A072852 A072853 A025192
Adjacent sequences: A160172 A160173 A160174 this_sequence A160176 A160177 A160178
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KEYWORD
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nonn
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AUTHOR
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Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), May 03 2009, May 06 2009
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