T. V. Raziman - cp's OEIS frontend

User: T. V. Raziman

T. V. Raziman has authored 2 sequences.

A319366 Number of 6 X n binary matrices such that any 2 rows have a common 1.

1, 127, 14197, 1527655, 154708741, 14581420567, 1282928605477, 106281575400295, 8370106554738181, 632240233746846007, 46159332156459328357, 3278558540783856976135, 227767526682511220042821, 15545657368091391819871447, 1046175606578621216182684837

Offset: 1

T. V. Raziman, Sep 17 2018

nonn

Mathematics Stack Exchange, An interesting combinatorics problem
Quora, How many ways are there to set N people into M groups so that every two groups have at least one common member?

Cf. A051587, A051588, A051589.

a(n) = 64^n - 15*48^n + 60*40^n - 15*36^n + 30*34^n - 6*33^n - 200*32^n - 180*30^n + 585*28^n + 45*27^n + 60*26^n + 150*25^n - 660*24^n - 360*23^n + 168*22^n - 585*21^n + 1245*20^n + 1665*19^n - 1965*18^n - 2100*17^n + 2170*16^n + 1325*15^n - 1770*14^n - 420*13^n + 1533*12^n - 1105*11^n + 435*10^n - 105*9^n + 15*8^n - 7^n (proved in the Quora answer).

A303050 Number of 2n-digit decimal numbers without leading zeros where each digit appears an even number of times.

Original entry on oeis.org

9, 252, 10944, 617472, 41457024, 3141499392, 259346018304, 22749987520512, 2082519895670784, 196336888097144832, 18885576885968830464, 1841197721072909156352, 181107406524439376953344, 17918621160090649673859072, 1779590652288735614991335424

Offset: 1

T. V. Raziman, Apr 17 2018

			For n=1, the a(1)=9 numbers are 11, 22, 33, ..., 88, 99.
For n=2, the a(2)=252 numbers are 1001, 1010, 1100, 1111, 1122, 1212, 1221, ..., 9988, 9999.

T. V. Raziman, Table of n, a(n) for n = 1..30
Quora, How many 2n digit numbers are there such that each digit is repeated even (possibly 0) times?
Index entries for linear recurrences with constant coefficients, signature (220,-16368,489280,-5395456,14745600).

LinearRecurrence[{220, -16368, 489280, -5395456, 14745600}, {9, 252, 10944, 617472, 41457024}, 20] (* Paolo Xausa, Mar 10 2024 *)

a(n) = 9/10 * 1/(2^10) * (2 * 10^(2n) + 20 * 8^(2n) + 90 * 6^(2n) + 240 * 4^(2n) + 420 * 2^(2n)) (proved in the Quora answers).

G.f.: -9 *(1111680*x^4 -229888*x^3 +11424*x^2 -192*x +1) *x / ((100*x-1) *(4*x-1) *(36*x-1) *(64*x-1) *(16*x-1)). - Alois P. Heinz, Apr 17 2018

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User: T. V. Raziman

A319366 Number of 6 X n binary matrices such that any 2 rows have a common 1.

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A303050 Number of 2n-digit decimal numbers without leading zeros where each digit appears an even number of times.

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