Original entry on oeis.org
1, 1, 3, 9, 24, 65, 177, 481, 1308, 3555, 9664, 26269, 71406, 194103, 527625, 1434235, 3898654, 10597641, 28807374, 78306562, 212859305, 578611580, 1572829344, 4275393425, 11621724256, 31591121861, 85873572496, 233428571660, 634524644587, 1724816811090, 4688538195006, 12744768177522
Offset: 0
(1, 1, 3, 9) convolved with (1, 2, 3, 4) = (4 + 3 + 6 + 9 ) = 22 = A024581(3).
- Steve Butler, R. L. Graham and Nan Zang, Jumping Sequences, Journal of Integer Sequences, Vol. 11, 2008, 08.4.5.
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lista(nn) = {my(va = vector(nn), vc = vector(nn)); va[1] = 1; for (n=1, nn, if (n > 1, va[n] = round(exp(1)*va[n-1])); vc[n] = va[n] - sum(k=1, n-1, vc[k]*(n-k+1));); vc;} \\ Michel Marcus, Jan 27 2019
A331028
Partition the terms of the harmonic series into groups sequentially so that the sum of each group is equal to or minimally greater than 1; then a(n) is the number of terms in the n-th group.
Original entry on oeis.org
1, 3, 8, 22, 60, 163, 443, 1204, 3273, 8897, 24184, 65739, 178698, 485751, 1320408, 3589241, 9756569, 26521104, 72091835, 195965925, 532690613, 1448003214, 3936080824, 10699376979, 29083922018, 79058296722, 214902731368, 584166189564, 1587928337892, 4316436745787
Offset: 1
a(1)=1 because 1 >= 1,
a(2)=3 because 1/2 + 1/3 + 1/4 = 1.0833... >= 1, etc.
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default(realprecision, 10^5); e=exp(1);
lista(nn) = {my(r=1); print1(r); for(n=2, nn, print1(", ", -r+(r=floor(e*r+(e+1)/2+(e-1/e)/(24*(r+1/2)))))); } \\ Jinyuan Wang, Mar 31 2020
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x = 0.0
y = 0.0
for i in range(1,100000000000000000000000):
y += 1
x = x + 1/i
if x >= 1:
print(y)
y = 0
x = 0
A153583
Convolution triangle by rows, A004736 * (A153582 * 0^(n-k)).
Original entry on oeis.org
1, 2, 1, 3, 2, 3, 4, 3, 6, 9, 5, 4, 9, 18, 24, 6, 5, 12, 27, 48, 65, 7, 6, 15, 36, 72, 130, 177, 8, 7, 18, 45, 96, 195, 354, 481, 9, 8, 21, 54, 120, 260, 531, 962, 1308, 10, 9, 24, 63, 144, 325, 708, 1443, 2616, 3555, 11, 10, 27, 72, 168, 390, 885, 1924, 3924, 7110, 9664
Offset: 0
First few rows of the triangle =
1;
2, 1;
3, 2, 3;
4, 3, 6, 9;
5, 4, 9, 18, 24;
6, 5, 12, 27, 48, 65;
7, 6, 15, 36, 72, 130, 177;
8, 7, 18, 45, 96, 195, 354, 481;
9, 8, 21, 54, 120, 260, 531, 962, 1308;
10, 9, 24, 63, 144, 325, 708, 1443, 2616, 3555;
...
Row 3 = (4, 3, 6, 9) = termwise products of (4, 3, 2, 1) and (1, 1, 3, 9);
where A153582 = (1, 1, 3, 9, 24, 65,...).
- Steve Butler, R. L. Graham & Nan Zang, Jumping Sequences, Journal of Integer Sequences, Vol. 11, 2008, 08.4.5.
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tabl(nn) = {my(va = vector(nn), vc = vector(nn)); va[1] = 1; for (n=1, nn, if (n > 1, va[n] = round(exp(1)*va[n-1])); vc[n] = va[n] - sum(k=1, n-1, vc[k]*(n-k+1)); print(vector(n, k, vc[k]*(n-k+1))););} \\ Michel Marcus, Jan 28 2019
A095716
a(n) = integer nearest Pi*a(n-1), where a(0) = 1.
Original entry on oeis.org
1, 3, 9, 28, 88, 276, 867, 2724, 8558, 26886, 84465, 265355, 833637, 2618948, 8227668, 25847981, 81203827, 255109346, 801449647, 2517828323, 7909990963, 24849969499, 78068481620, 245259368334, 770505029782, 2420612941117
Offset: 0
Herman Jamke (hermanjamke(AT)fastmail.fm), Jul 07 2004
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a[0] = 1; a[n_] := Round[Pi*a[n - 1]]; Table[a[n], {n, 0, 30}] (* Clark Kimberling, Aug 18 2012 *)
Showing 1-4 of 4 results.
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