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Search: id:A026377
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| A026377 |
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a(n) = number of integer strings s(0),...,s(n) counted by array T in A026374 that have s(n)=4; also a(n)=T(2n,n-2). |
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3
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| 1, 9, 58, 330, 1770, 9198, 46928, 236736, 1185645, 5909805, 29362806, 145570230, 720606705, 3563543025, 17610412600, 86989143480, 429579843435, 2121099312195, 10472653252550, 51708363376950, 255326054688320
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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Number of lattice paths from (0,0) to (2n,4), using steps U=(1,1), D=(1,-1), and at even levels(zero, positive, and negative) also H=(2,0). Example: a(3)=9 because we have UUUUUD, UUUUDU, UUUDUU, UUDUUU, UDUUUU, DUUUUU, HUUUU, UUHUU, and UUUUH. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 30 2004
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FORMULA
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a(n)=[t^(n+2)](1+3t+t^2)^n. a(n)=sum(3^(2j-n-2)*binomial(n, j)*binomial(j, n+2-j), j=ceil((n+2)/2)..n). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 30 2004
E.g.f. : exp(3x)BesselI(2, 2x); a(n)=sum{k=0..n, binomial(n, k)binomial(2k, k+2)}. - Paul Barry (pbarry(AT)wit.ie), Sep 20 2004
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CROSSREFS
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Sequence in context: A018218 A026750 A009034 this_sequence A016209 A129173 A055423
Adjacent sequences: A026374 A026375 A026376 this_sequence A026378 A026379 A026380
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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