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Search: id:A081495
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| A081495 |
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Start with Pascal's triangle; form a rhombus by sliding down n steps from top on both sides then sliding down inwards to complete the rhombus and then deleting the inner numbers; a(n) = sum of entries on perimeter of rhombus. |
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+0
4
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| 1, 5, 17, 55, 189, 681, 2519, 9451, 35765, 136153, 520695, 1998745, 7696467, 29716025, 115000947, 445962899, 1732525861, 6741529113, 26270128535, 102501265057, 400411345659, 1565841089321, 6129331763923, 24014172955545
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(0)=1 for n>0 a(n)=binomial(2*n, n)-binomial(2*n-2, n-1)+2*n-3 - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 10 2003
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EXAMPLE
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The rhombus pertaining to n = 4 is obtained from the solid rhombus
.....1
...1...1
.1...2...1
1..3...3...1
..4..6...4
...10..10
.....20
giving
.....1
...1...1
.1.......1
1..........1
..4......4
...10..10
.....20
and the sum of all the numbers is 55, a(4) = 55.
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CROSSREFS
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Cf. A081494, A081496, A081497.
Adjacent sequences: A081492 A081493 A081494 this_sequence A081496 A081497 A081498
Sequence in context: A034346 A055419 A027091 this_sequence A112410 A112044 A027030
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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 Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 10 2003
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