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Search: id:A081496
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| A081496 |
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Start with Pascal's triangle; a(n) is the sum of the numbers on the periphery of the n-th central rhombus containing exactly 4 numbers. |
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+0
4
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| 5, 14, 46, 160, 574, 2100, 7788, 29172, 110110, 418132, 1595620, 6113744, 23505356, 90633800, 350351640, 1357278300, 5268292830, 20483876820, 79765662900, 311038321440, 1214362277700, 4746455801880, 18570960418920, 72728638093800
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n) = (9*n-4)*Catalan(n-1) = (9*n-4)*binomial(2*(n-1), (n-1))/n - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 20 2004
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EXAMPLE
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The first three rhombuses are
...1...........2.........6
.1...1.......3...3.....10..10
...2......,....6.....,...20
and the corresponding sums are a(1) =5, a(2) =14 and a(3) =46.
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MAPLE
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seq((9*n-4)*binomial(2*(n-1), (n-1))/n, n=1..26); (C. Ronaldo)
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CROSSREFS
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Cf. A081494, A081495, A081497.
Adjacent sequences: A081493 A081494 A081495 this_sequence A081497 A081498 A081499
Sequence in context: A077335 A126729 A098730 this_sequence A075827 A134418 A107242
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 25 2003
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EXTENSIONS
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More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 20 2004
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