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Search: id:A131075
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| A131075 |
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First subdiagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 8) < 4, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j. |
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+0
5
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| 1, 2, 4, 7, 11, 16, 22, 30, 46, 92, 232, 628, 1652, 4096, 9544, 21000, 43912, 87824, 169120, 315952, 578096, 1048576, 1913440, 3567072, 6874336, 13748672, 28384384, 59797312, 126906176, 268435456, 561834112, 1158971520, 2353246336
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also first differences of main diagonal A129961.
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FORMULA
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a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 7, a(5) = 11; for n > 5, a(n) = 6*a(n-1)-14*a(n-2)+16*a(n-3)-10*a(n-4)+4*a(n-5).
G.f.: (1-4*x+6*x^2-5*x^3+3*x^4)/((1-2*x)*(1-4*x+6*x^2-4*x^3+2*x^4)).
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EXAMPLE
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For first seven rows of T see A131074 or A129961.
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PROGRAM
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(MAGMA) m:=34; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do if (j-1) mod 8 lt 4 then M[j, 1]:=1; end if; end for; for k:=2 to m do for j:=k to m do M[j, k]:=M[j-1, k-1]+M[j, k-1]; end for; end for; [ M[n+1, n]: n in [1..m-1] ];
(PARI) {m=33; v=concat([1, 2, 4, 7, 11], vector(m-5)); for(n=6, m, v[n]=6*v[n-1]-14*v[n-2]+16*v[n-3]-10*v[n-4]+4*v[n-5]); v}
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CROSSREFS
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Cf. A131074 (T read by rows), A129961 (main diagonal of T), A131076 (row sums of T), A131077 (antidiagonal sums of T). First through sixth column of T are in A131078, A131079, A131080, A131081, A131082, A131083 resp.
Sequence in context: A000124 A098574 A005689 this_sequence A133523 A114805 A000601
Adjacent sequences: A131072 A131073 A131074 this_sequence A131076 A131077 A131078
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KEYWORD
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nonn
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AUTHOR
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Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), following a suggestion of Paul Curtz (bpcrtz(AT)free.fr), Jun 14 2007
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