login
A238941
Triangle T(n,k), read by rows given by (1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
1
1, 1, 1, 2, 3, 1, 5, 8, 4, 1, 13, 21, 13, 6, 1, 34, 55, 40, 25, 7, 1, 89, 144, 120, 90, 33, 9, 1, 233, 377, 354, 300, 132, 51, 10, 1, 610, 987, 1031, 954, 483, 234, 62, 12, 1, 1597, 2584, 2972, 2939, 1671, 951, 308, 86, 13, 1, 4181, 6765, 8495, 8850, 5561, 3573, 1345, 480, 100, 15, 1
OFFSET
0,4
COMMENTS
Row sums are A025192(n).
LINKS
Indranil Ghosh, Rows 0..100, flattened
FORMULA
G.f. for the column k: x^k*(1-2*x)^A059841(k)/(1-3*x+x^2)^A008619(k).
G.f.: (1-2*x+x*y)/(1-3*x+x^2-x^2*y^2).
T(n,k) = 3*T(n-1,k) + T(n-2,k-2) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.
Sum_{k = 0..n} T(n,k)*x^k = A000007(n), A001519(n), A025192(n), A030195(n+1) for x = -1, 0, 1, 2 respectively.
Sum_{k = 0..n} T(n,k)*3^k = A015525(n) + A015525(n+1).
EXAMPLE
Triangle begins:
1;
1, 1;
2, 3, 1;
5, 8, 4, 1;
13, 21, 13, 6, 1;
34, 55, 40, 25, 7, 1;
89, 144, 120, 90, 33, 9, 1;
233, 377, 354, 300, 132, 51, 10, 1;
MATHEMATICA
nmax=10; Column[CoefficientList[Series[CoefficientList[Series[(1 - 2*x + x*y)/(1 - 3*x + x^2 - x^2*y^2), {x, 0, nmax }], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 14 2017 *)
CROSSREFS
Cf. Columns: A001519, A001906, A238846, A001871.
Cf. Diagonals: A000012, A032766.
Sequence in context: A292770 A242107 A242108 * A247582 A359795 A224652
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Mar 07 2014
EXTENSIONS
Data section corrected and extended by Indranil Ghosh, Mar 14 2017
STATUS
approved