A287919 - OEIS

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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

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

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