A058877 -id:A058877 - cp's OEIS frontend

A344215 a(n) = n*(3^(n-1) - 2^(n-1)).

0, 0, 2, 15, 76, 325, 1266, 4655, 16472, 56745, 191710, 638275, 2101188, 6855485, 22205834, 71498775, 229058224, 730680145, 2322163638, 7356008555, 23234743580, 73200452325, 230081633122, 721667902015, 2259234965256, 7060318981625, 22028631430286, 68628565425555, 213512971483252

Offset: 0

Enrique Navarrete, May 11 2021

a(n) is the number of quaternary strings of length n that contain one 0 and at least one 1.

For ternary strings with this property see A058877; for binary strings see A199969.

			a(3)=15 since the strings are the 3 permutations of 011, the 6 permutations of 012 and the 6 permutations of 013.

Index entries for linear recurrences with constant coefficients, signature (10,-37,60,-36).

Cf. A058877, A199969.

LinearRecurrence[{10, -37, 60, -36}, {0, 0, 2, 15}, 29] (* Amiram Eldar, May 11 2021 *)
Table[n(3^(n-1)-2^(n-1)),{n,0,30}] (* Harvey P. Dale, Mar 13 2022 *)

E.g.f.: x*(exp(3*x) - exp(2*x)).

G.f.: x^2*(2 - 5*x)/(1 - 5*x + 6*x^2)^2. - Stefano Spezia, May 12 2021

A348864 a(n) is the number of multiplications required to compute the permanent of general n X n matrices using trellis method with normalization.

Original entry on oeis.org

0, 4, 12, 32, 70, 162, 350, 800, 1746, 3950, 8602, 19164, 41392, 90846, 194490, 421568, 895594, 1922022, 4057298, 8638580, 18140640, 38378054, 80244562, 168877272, 351827100, 737208082, 1531123830, 3196464740, 6621247636, 13779365430, 28477354354, 59102191488, 121898268954

Offset: 1

Stefano Spezia, Nov 02 2021

nonn

Han Mao Kiah, Alexander Vardy and Hanwen Yao, Computing Permanents on a Trellis, arXiv:2107.07377 [cs.IT], 2021.

Cf. A001787, A002378, A058877, A100071.

a[n_]:=n 2^(n-1)-Ceiling[n/2]Binomial[n,Floor[n/2]]+n^2-n; Array[a,33]

a(n) = n*2^(n-1) - ceil(n/2)*binomial(n, floor(n/2)) + n^2 - n; \\ Michel Marcus, Nov 03 2021

a(n) = n*2^(n-1) - ceiling(n/2)*binomial(n, floor(n/2)) + n^2 - n (see Theorem 6, p. 11 in Kiah et al.).
a(n) = A001787(n) - A100071(n) + A002378(n-1).
O.g.f.: x*(1/(1 - 2*x)^2 + 2*x/(1 - x)^3 - 1/((1 - 2*x)*sqrt(1 - 4*x^2))).
E.g.f.: exp(x)*x*(exp(x) + x) - (1 + x)*BesselI(1, 2*x) - x*BesselI(2, 2*x).
D-finite with recurrence (n-1)*(n-2)*(n-4)*(3*n-23)*a(n) -3*(n -2)*(3*n^3-34*n^2+91*n-20)*a(n-1) -2*(n-1)*(n-3)*(3*n^2 -47*n+164)*a(n-2) +12*(3*n-22)*(n-1)*(n-2)*(n-4)*a(n-3) -8*(3*n-20)*(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Mar 06 2022

cp's OEIS Frontend

A344215 a(n) = n*(3^(n-1) - 2^(n-1)).

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