A287919 Square array T(0,n) = prime(n) and T(m+1,n) = T(m,n) + T(m,n+1), m >= 0, n >= 1, read by falling antidiagonals.

2, 3, 5, 5, 8, 13, 7, 12, 20, 33, 11, 18, 30, 50, 83, 13, 24, 42, 72, 122, 205, 17, 30, 54, 96, 168, 290, 495, 19, 36, 66, 120, 216, 384, 674, 1169, 23, 42, 78, 144, 264, 480, 864, 1538, 2707, 29, 52, 94, 172, 316, 580, 1060, 1924, 3462, 6169

Offset

0,1

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Example

The array starts:
[0]    2    3    5     7    11    13    17    19    23    29 ... (A000040)
[1]    5    8   12    18    24    30    36    42    52    60 ... (A001043)
[2]   13   20   30    42    54    66    78    94   112   128 ... (A096277)
[3]   33   50   72    96   120   144   172   206   240   274 ... (A096278)
[4]   83  122  168   216   264   316   378   446   514   582 ... (A096279)
[5]  205  290  384   480   580   694   824   960  1096  1226 ...
[6]  495  674  864  1060  1274  1518  1784  2056  2322  2570 ...
[7] 1169 1538 1924  2334  2792  3302  3840  4378  4892  5380 ...
...
First column is A007443: binomial transform of primes.
Second column is A178167: binomial transform of odd primes.

Mathematica

A287919list[dmax_]:=With[{a=Reverse[NestList[ListConvolve[{1, 1}, #]&, Prime[Range[dmax]], dmax-1]]}, Array[Reverse[Diagonal[a, #]]&, dmax, 1-dmax]];
A287919list[10] (* Generates 10 antidiagonals *) (* Paolo Xausa, Oct 31 2023 *)

Prog

(PARI) A287919(m, n)=sum(k=0, m, prime(n+k)*binomial(m, k))
/* read by antidiagonals */ for(m=0, 13, for(n=0, m, print1(A287919(n, m-n+1)", ")))

Crossrefs

Rows and columns include A001043, A096277-A096279, A007443, A178167.

Sequence in context: A238007 A204207 A354704 * A138181 A006447 A014237

Adjacent sequences: A287916 A287917 A287918 * A287920 A287921 A287922

Keyword

nonn,easy,tabl

Author

M. F. Hasler, Jun 02 2017

Status

approved