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Search: id:A065942
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| 1, 1, 3, 4, 15, 21, 84, 120, 495, 715, 3003, 4368, 18564, 27132, 116280, 170544, 735471, 1081575, 4686825, 6906900, 30045015, 44352165, 193536720, 286097760, 1251677700, 1852482996, 8122425444, 12033222880, 52860229080, 78378960360
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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When viewed as (1,1),(3,4),(15,21),... this represents a shallow staircase on Pascal's triangle, arranged as a square array. - Paul Barry (pbarry(AT)wit.ie), Mar 11 2003
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REFERENCES
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Henry W. Gould, "A Variant of Pascal's Triangle", The Fibonacci Quarterly,3;4 Dec. 1965, pp. 257-271.
Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", John Wiley and Sons, 2001 (Chapter 14)
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FORMULA
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Binomial(n-floor((n/2+1)/2), floor(n/4))
a(n)=sum(k=0, ceil(n/2), binomial(n+k, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 06 2004
a(n)=binomial(n+floor(n/2), n). - Paul Barry (pbarry(AT)wit.ie), May 18 2004
a(n)=sum{k=0..floor(n/2), binomial(n-1+k, k)}. - Paul Barry (pbarry(AT)wit.ie), Jul 06 2004
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CROSSREFS
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Cf. A065941 (complete triangle)
Sequence in context: A041819 A095799 A109926 this_sequence A036759 A081405 A167367
Adjacent sequences: A065939 A065940 A065941 this_sequence A065943 A065944 A065945
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KEYWORD
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nonn
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Nov 29 2001
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