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 A129961 Main diagonal 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. 5
 1, 2, 4, 8, 15, 26, 42, 64, 94, 140, 232, 464, 1092, 2744, 6840, 16384, 37384, 81296, 169120, 338240, 654192, 1232288, 2280864, 4194304, 7761376, 14635712, 28384384, 56768768, 116566080, 243472256, 511907712, 1073741824, 2232713344 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First column is periodically 1 1 1 1 0 0 0 0 (see A131078). First subdiagonal is 1, 2, 4, 7, 11, 16, 22, ... (see A131075); next subdiagonals are 1, 2, 3, 4, 5, 6, 8, 16, 46, 140, ..., 1, 1, 1, 1, 1, 2, 8, 30, 94, 256, ..., 0, 0, 0, 0, 1, 6, 22, 64, 162, 372, ..., 0, 0, 0, 1, 5, 16, 42, 98, 210, 420, ...., 0, 0, 1, 4, 11, 26, 56, 112, 210, 372, ..., 0, 1, 3, 7, 15, 30, 56, 98, 162, 256, ...,1, 2, 4, 8, 15, 26, 42, 64, 94, 140, ... . Main diagonal and eighth subdiagonal agree; generally j-th subdiagonal equals (j+8)-th subdiagonal. Antidiagonal sums are 1, 1, 3, 3, 6, 5, 11, ... (see A131077). LINKS FORMULA G.f.: x*(1-x)^4/((1-2*x)*(1-4*x+6*x^2-4*x^3+2*x^4)). a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 8, a(5) = 15; 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). Binomial transform of A131078. - Klaus Brockhaus, Jun 17 2007 EXAMPLE First seven rows of T are [ 1 ] [ 1, 2 ] [ 1, 2, 4 ] [ 1, 2, 4, 8 ] [ 0, 1, 3, 7, 15 ] [ 0, 0, 1, 4, 11, 26 ] [ 0, 0, 0, 1, 5, 16, 42 ]. PROG (PARI) {m=33; v=concat([1, 2, 4, 8, 15], 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} \\ Klaus Brockhaus, Jun 14 2007 (MAGMA) m:=33; 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, n]: n in [1..m] ]; // Klaus Brockhaus, Jun 14 2007 (MAGMA) m:=33; S:=[ [1, 1, 1, 1, 0, 0, 0, 0][(n-1) mod 8 + 1]: n in [1..m] ]; [ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; // Klaus Brockhaus, Jun 17 2007 CROSSREFS Cf. A129339, A131074 (T read by rows), A131075 (first subdiagonal 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: A089140 A204555 A000125 * A133551 A114226 A210063 Adjacent sequences:  A129958 A129959 A129960 * A129962 A129963 A129964 KEYWORD nonn AUTHOR Paul Curtz, Jun 10 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, Jun 14 2007 G.f. corrected by Klaus Brockhaus, Oct 15 2009 STATUS approved

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Last modified February 29 02:35 EST 2020. Contains 332353 sequences. (Running on oeis4.)