A370965 -id:A370965

Search: a370965 -id:a370965

Displaying 1-3 of 3 results found.

page 1

A370962

a(n) = number of "lonesum" 2 X 2 X n tensors.

+10
3

1, 14, 104, 644, 3668, 19964, 105764, 550844, 2836868, 14498204, 73695524, 373141244, 1883894468, 9490820444, 47735267684, 239788294844, 1203351134468, 6034279718684, 30241150798244, 151483730475644, 758527460524868, 3797063240264924, 19002992063903204

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Don Knuth, Parades and poly-Bernoulli bijections, Mar 31 2024. See (19.11).

Filip Stappers, Problems concerning parades and poly-Bernoulli numbers, 2024. See Problem 9.

Index entries for linear recurrences with constant coefficients, signature (14,-71,154,-120).

FORMULA

From Filip Stappers, Aug 27 2024: (Start)

a(n) = 8*5^n - 4*4^n - 4*3^n + 2^n.

G.f.: (1-21*z^2-28*z^3)/((1-5*z)*(1-4*z)*(1-3*z)*(1-2*z)). (End)

CROSSREFS

Cf. A370963, A370964, A370965.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 04 2024

EXTENSIONS

a(7) from Michael S. Branicky, Apr 05 2024

a(8) from Michael S. Branicky, Apr 06 2024

a(9) from Michael S. Branicky, Apr 08 2024

a(10) from Michael S. Branicky, Apr 27 2024

a(0) and more terms from Filip Stappers, Aug 27 2024

STATUS

approved

A370963

a(n) = number of "lonesum" n X n X n tensors.

+10
3

2, 104, 126164

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..3.

Don Knuth, Parades and poly-Bernoulli bijections, Mar 31 2024. See (19.11).

CROSSREFS

Cf. A370962, A370964, A370965.

KEYWORD

nonn,more,bref

AUTHOR

N. J. A. Sloane, Apr 04 2024

STATUS

approved

A370964

a(n) = number of "weakly lonesum" 2 X 2 X n tensors.

+10
3

1, 16, 254, 4006, 62834, 980926, 15251714, 236305246, 3649992194, 56225671966, 864046126274, 13249946549086, 202798763405954, 3098675363464606, 47273845225223234, 720219685203906526, 10958863373616410114, 166560903942055522846, 2528904905860164038594

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

Don Knuth, Parades and poly-Bernoulli bijections, Mar 31 2024. See (19.13).

Filip Stappers, Problems concerning parades and poly-Bernoulli numbers, 2024. See Problem 9.

Index entries for linear recurrences with constant coefficients, signature (29,-210).

FORMULA

From Filip Stappers, Aug 25 2024: (Start)

a(n) = 2*15^n - 14^n.

G.f.: (1-13*z) / ((1-15*z)*(1-14*z)). (End)