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A329637
Square array A(n, k) = A329644(prime(n)^k), read by falling antidiagonals: (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ...
5
1, 1, 1, 4, -1, 1, 0, 4, -5, 1, 24, -16, 4, -13, 1, -8, 40, -48, 4, -29, 1, 104, -88, 72, -112, 4, -61, 1, -48, 184, -248, 136, -240, 4, -125, 1, 352, -400, 344, -568, 264, -496, 4, -253, 1, 80, 544, -1104, 664, -1208, 520, -1008, 4, -509, 1, 1424, -784, 928, -2512, 1304, -2488, 1032, -2032, 4, -1021, 1
OFFSET
1,4
FORMULA
A(n, k) = A329644(A182944(n, k)).
A(n, k) = A000079(n+k-1) - (A000225(n) * A329890(k)).
EXAMPLE
The top left corner of the array:
n p_n |k=1, 2, 3, 4, 5, 6, 7, 8, 9, 10
---------+----------------------------------------------------------------------
1 -> 2 | 1, 1, 4, 0, 24, -8, 104, -48, 352, 80,
2 -> 3 | 1, -1, 4, -16, 40, -88, 184, -400, 544, -784,
3 -> 5 | 1, -5, 4, -48, 72, -248, 344, -1104, 928, -2512,
4 -> 7 | 1, -13, 4, -112, 136, -568, 664, -2512, 1696, -5968,
5 -> 11 | 1, -29, 4, -240, 264, -1208, 1304, -5328, 3232, -12880,
6 -> 13 | 1, -61, 4, -496, 520, -2488, 2584, -10960, 6304, -26704,
7 -> 17 | 1, -125, 4, -1008, 1032, -5048, 5144, -22224, 12448, -54352,
8 -> 19 | 1, -253, 4, -2032, 2056, -10168, 10264, -44752, 24736, -109648,
9 -> 23 | 1, -509, 4, -4080, 4104, -20408, 20504, -89808, 49312, -220240,
10 -> 29 | 1, -1021, 4, -8176, 8200, -40888, 40984, -179920, 98464, -441424,
11 -> 31 | 1, -2045, 4, -16368, 16392, -81848, 81944, -360144, 196768, -883792,
PROG
(PARI)
up_to = 105;
A329890(n) = if(1==n, 1, sigma((2^n)-1)-sigma((2^(n-1))-1));
A329637sq(n, k) = ((2^(n+k-1)) - (((2^n)-1) * A329890(k)));
A329637list(up_to) = { my(v = vector(up_to), i=0); for(a=1, oo, for(col=1, a, i++; if(i > up_to, return(v)); v[i] = A329637sq(col, (a-(col-1))))); (v); };
v329637 = A329637list(up_to);
A329637(n) = v329637[n];
CROSSREFS
Rows 1-2: A329891, A329892 (from n>=1).
Column 1: A000012, Column 2: -A036563(n) (from n>=1), Column 3: A010709.
Sequence in context: A364026 A128760 A057884 * A276834 A016684 A324564
KEYWORD
sign,tabl
AUTHOR
Antti Karttunen, Nov 22 2019
STATUS
approved