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A161161 Irregular triangle of differences T(n,k) = A083906(n,k)-A083906(n-1,k) of q-Binomial coefficients. 2
1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 3, 5, 2, 2, 1, 1, 2, 3, 5, 7, 5, 4, 3, 1, 1, 1, 2, 3, 5, 7, 11, 8, 9, 7, 6, 2, 2, 1, 1, 2, 3, 5, 7, 11, 15, 14, 15, 15, 13, 11, 7, 4, 3, 1, 1, 1, 2, 3, 5, 7, 11, 15, 22, 21, 25, 25, 27, 23, 22, 15, 13, 8, 6, 2, 2, 1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 32, 37, 42, 44 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..93.

M. Isachenkov, I. Kirsch, V. Schomerus, Chiral Primaries in Strange Metals, arXiv preprint arXiv:1403.6857 [hep-th], 2014. See Eq. (4.6).

EXAMPLE

The differences between 5 3 4 3 1 and 4 2 2 yield row four : 1 1 2 3 1.

1;

1, 1;

1, 1, 2;

1, 1, 2, 3, 1;

1, 1, 2, 3, 5, 2, 2;

1, 1, 2, 3, 5, 7, 5,  4,  3,  1;

1, 1, 2, 3, 5, 7, 11, 8,  9,  7,  6,  2,  2;

1, 1, 2, 3, 5, 7, 11, 15, 14, 15, 15, 13, 11, 7, 4, 3, 1;

1, 1, 2, 3, 5, 7, 11, 15, 22, 21, 25, 25, 27, 23, 22, 15, 13, 8, 6, 2, 2;

MAPLE

A161161 := proc(n, m)

     A083906(n, m)-A083906(n-1, m) ;

end proc:

for n from 0 to 10 do

     for k from 0 to A033638(n)-1 do

         printf("%d, ", A161161(n, k)) ;

     od:

od: # R. J. Mathar, Jul 13 2012

MATHEMATICA

b[n_, k_] := b[n, k] = SeriesCoefficient[Sum[QBinomial[n, m, q], {m, 0, n}], {q, 0, k}];

T[n_, k_] := b[n, k] - b[n - 1, k];

Table[Table[T[n, k], {k, 0, n^2/4}], {n, 1, 10}] // Flatten (* Jean-Fran├žois Alcover, Nov 25 2017 *)

CROSSREFS

Cf. A002865 (antidiagonal sums), A000079 (row sums).

Sequence in context: A246028 A232186 A325757 * A136277 A133233 A174430

Adjacent sequences:  A161158 A161159 A161160 * A161162 A161163 A161164

KEYWORD

easy,nonn,tabf

AUTHOR

Alford Arnold, Jun 04 2009

STATUS

approved

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)