A055996 -id:A055996 - cp's OEIS frontend

A201780 Riordan array ((1-x)^2/(1-2x), x/(1-2x)).

1, 0, 1, 1, 2, 1, 2, 5, 4, 1, 4, 12, 13, 6, 1, 8, 28, 38, 25, 8, 1, 16, 64, 104, 88, 41, 10, 1, 32, 144, 272, 280, 170, 61, 12, 1, 64, 320, 688, 832, 620, 292, 85, 14, 1, 128, 704, 1696, 2352, 2072, 1204, 462, 113, 16, 1

Offset: 0

Philippe Deléham, Dec 05 2011

Diagonals ascending: 1, 0, 1, 1, 2, 2, 4, 5, 1, 8, 12, 4, ... (see A201509).

			Triangle begins:
  1;
  0,  1;
  1,  2,  1;
  2,  5,  4,  1;
  4, 12, 13,  6,  1;
  8, 28, 38, 25,  8,  1;

Benjamin Braun, W. K. Hough, Matching and Independence Complexes Related to Small Grids, arXiv preprint arXiv:1606.01204 [math.CO], 2016.
Wesley K. Hough, On Independence, Matching, and Homomorphism Complexes, (2017), Theses and Dissertations--Mathematics, 42.

Diagonals: A000012, A005843, A001844, A035597,
Columns: A034008, A045623, A084851, A055585,
Row sums: A052156

CoefficientList[#, y]& /@ CoefficientList[(1-x)^2/(1-(y+2)*x) + O[x]^10, x] // Flatten (* Jean-François Alcover, Nov 03 2018 *)

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) with T(0,0) = 0, T(1,0) = 0, T(2,0) = 0 and T(n,k)= 0 if k < 0 or if n < k.
Sum_{k=0..n} T(n,k)*x^k = A154955(n+1), A034008(n), A052156(n), A055841(n), A055842(n), A055846(n), A055270(n), A055847(n), A055995(n), A055996(n), A056002(n), A056116(n) for x = -1,0,1,2,3,4,5,6,7,8,9,10 respectively.
G.f.: (1-x)^2/(1-(y+2)*x).

A056116 a(n) = 121*12^(n-2), a(0)=1, a(1)=10.

Original entry on oeis.org

1, 10, 121, 1452, 17424, 209088, 2509056, 30108672, 361304064, 4335648768, 52027785216, 624333422592, 7492001071104, 89904012853248, 1078848154238976, 12946177850867712, 155354134210412544

Offset: 0

Barry E. Williams, Jul 04 2000

For n >= 2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8,9,10,11,12} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7,8,9,10,11,12} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan Janjic, Apr 19 2007

a(n) is the number of generalized compositions of n when there are 11*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (12).

Cf. A055996, A056002.

concatenation([1,10], List([2..20], n-> 121*12^(n-2) )); # G. C. Greubel, Jan 18 2020

[1,10] cat [121*12^(n-2): n in [2..20]]; // G. C. Greubel, Jan 18 2020

1,10, seq( 121*12^(n-2), n=2..20); # G. C. Greubel, Jan 18 2020

LinearRecurrence[{12},{1,10,121},20] (* Harvey P. Dale, Oct 20 2015 *)

concat([1, 10], vector(20, n, 121*12^(n-1) )) \\ G. C. Greubel, Jan 18 2020

[1,10]+[121*12^(n-2) for n in (2..20)] # G. C. Greubel, Jan 18 2020

a(n) = 12*a(n-1) + (-1)^n*C(2, 2-n).
G.f.: (1-x)^2/(1-12*x).
a(n) = Sum_{k=0..n} A201780(n,k)*10^k. - Philippe Deléham, Dec 05 2011
E.g.f.: (23 - 12*x + 121*exp(12*x))/144. - G. C. Greubel, Jan 18 2020

More terms from James Sellers, Jul 04 2000

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A201780 Riordan array ((1-x)^2/(1-2x), x/(1-2x)).

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A056116 a(n) = 121*12^(n-2), a(0)=1, a(1)=10.

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