A045927 -id:A045927 - cp's OEIS frontend

A045926 All digits even and nonzero.

2, 4, 6, 8, 22, 24, 26, 28, 42, 44, 46, 48, 62, 64, 66, 68, 82, 84, 86, 88, 222, 224, 226, 228, 242, 244, 246, 248, 262, 264, 266, 268, 282, 284, 286, 288, 422, 424, 426, 428, 442, 444, 446, 448, 462, 464, 466, 468, 482, 484, 486, 488, 622, 624, 626, 628, 642

Offset: 1

Felice Russo

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A045927, A014261, A014263, A192370.

a045926 n = a045926_list !! (n-1)
a045926_list = filter (all (`elem` "2468") . show) [2, 4..]
-- Reinhard Zumkeller, Jan 01 2013

def A045926(n):
    m = (3*n+1).bit_length()-1>>1
    return int(''.join((str(((3*n+1-(1<<(m<<1)))//(3<<((m-1-j)<<1))&3)+1) for j in range(m))))<<1 # Chai Wah Wu, Feb 08 2023

a(n) = 2 * A084544(n). - Reinhard Zumkeller, Jan 01 2013

More terms from Patrick De Geest, Jun 15 1999

A094953 Triangle T(n,m) read by rows: number of rises (drops) in the compositions of n with m parts, m>=2.

Original entry on oeis.org

1, 1, 2, 2, 4, 3, 2, 8, 9, 4, 3, 12, 21, 16, 5, 3, 18, 39, 44, 25, 6, 4, 24, 66, 96, 80, 36, 7, 4, 32, 102, 184, 200, 132, 49, 8, 5, 40, 150, 320, 430, 372, 203, 64, 9, 5, 50, 210, 520, 830, 888, 637, 296, 81, 10, 6, 60, 285, 800, 1480, 1884, 1673, 1024, 414, 100, 11, 6

Offset: 2

Ralf Stephan, May 26 2004

			1
1 2
2 4 3
2 8 9 4
3 12 21 16 5
3 18 39 44 25 6
4 24 66 96 80 36 7

S. Heubach and T. Mansour, Counting rises, levels and drops in compositions, arXiv:math/0310197 [math.CO], 2003.

Columns 2-4 (+-offset) are A004526, A007590, A007518.
Row sums are A045883, diagonals include n, n^2, (n-1)(n^2-n+2)/2, (n-1)^2(n^+n+6), etc.
Cf. A045927.

T[n_, m_] := SeriesCoefficient[(m-1)x^(m+1)/(1+x)/(1-x)^m, {x, 0, n+1}];
Table[T[n, m], {n, 2, 13}, {m, 2, n}] // Flatten (* Jean-François Alcover, Dec 03 2018 *)

T(n,m)=polcoeff((m-1)*x^(m+1)/(1+x)/(1-x)^m,n)

G.f. of m-th column: [(m-1)x^(m+1)]/[(1+x)(1-x)^m].

cp's OEIS Frontend

A045926 All digits even and nonzero.

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