login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A131025 Antidiagonal sums of triangular array T: T(j,1) = 1 for ((j-1) mod 6) < 3, else 0; T(j,k) = T(j-1,k-1) + T(j-1,k) for 2 <= k <= j. 5
1, 1, 3, 2, 5, 3, 9, 6, 16, 11, 27, 22, 50, 50, 101, 114, 215, 255, 471, 552, 1024, 1145, 2169, 2290, 4460, 4460, 8921, 8556, 17477, 16383, 33861, 31674, 65536, 62255, 127791, 124510, 252302, 252302, 504605, 514446, 1019051, 1048575, 2067627 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..6644

Scott M. Bailey and Donald M. Larson, The A(1)-module structure of the homology of Brown-Gitler spectra, arXiv:2107.01316 [math.AT], 2021.

FORMULA

G.f.: (1-3*x^2+2*x^4+2*x^6-2*x^8+x^9)/((1-x)*(1+x)*(1-x+x^2)*(1-2*x^2)*(1-3*x^2+3*x^4)).

EXAMPLE

For first seven rows of T see A131022 or A129339.

MATHEMATICA

CoefficientList[Series[(1 - 3 x^2 + 2 x^4 + 2 x^6 - 2 x^8 + x^9)/((1 - x)*(1 + x)*(1 - x + x^2)*(1 - 2 x^2)*(1 - 3 x^2 + 3 x^4)), {x, 0, 42}], x] (* Michael De Vlieger, Oct 26 2021 *)

PROG

(PARI) {m=43; M=matrix(m, m); for(j=1, m, M[j, 1]=if((j-1)%6<3, 1, 0)); for(k=2, m, for(j=k, m, M[j, k]=M[j-1, k-1]+M[j, k-1])); for(j=1, m, print1(sum(k=1, (j+1)\2, M[j-k+1, k]), ", "))}

(Magma) m:=43; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do if (j-1) mod 6 lt 3 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[j-k+1, k]: k in [1..(j+1) div 2] ]: j in [1..m] ];

CROSSREFS

Cf. A131022 (T read by rows), A129339 (main diagonal of T), A131023 (first subdiagonal of T), A131024 (row sums of T). First through sixth column of T are in A088911, A131026, A131027, A131028, A131029, A131030 resp.

Sequence in context: A045766 A281668 A132817 * A340702 A070151 A331847

Adjacent sequences: A131022 A131023 A131024 * A131026 A131027 A131028

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, following a suggestion of Paul Curtz, Jun 10 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 7 02:40 EST 2023. Contains 360111 sequences. (Running on oeis4.)