A056413
Number of step cyclic shifted sequences using a maximum of five different symbols.
Original entry on oeis.org
5, 15, 35, 120, 201, 1505, 2015, 14070, 37085, 246753, 445515, 5205790, 7832185, 72703645, 254689657, 1196213445, 2805046965, 35322811755, 55770979195, 596439735024, 1892294578755, 10837223014665, 23559159229935, 310484619147940, 596046508875701, 4776013513099405, 15330413466776835, 110874578286500410
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
-
M[j_, L_] := Module[{m = 1}, While[Sum[ j^i, {i, 0, m - 1}] ~Mod~ L != 0, m++]; m]; c[j_, t_, n_] := Sum[ 1/M[j, n / GCD[n, u*(j - 1) + t] ], {u, 0, n - 1} ]; CB[n_, k_] = If [n == 1, k, 1/(n*EulerPhi[n]) * Sum[ If[1 == GCD[n, j], k^c[j, t, n], 0] , {t, 0, n-1}, {j, 1, n-1}]]; Table[ Print[ cb = CB[n, 5]]; cb, {n, 1, 28}] (* Jean-François Alcover, Dec 04 2015, after Joerg Arndt *)
-
\\ see p.3 of the Dokovic et al. reference
M(j, L)={my(m=1); while ( sum(i=0, m-1, j^i) % L != 0, m+=1 ); m; }
c(j, t, n)=sum(u=0,n-1, 1/M(j, n / gcd(n, u*(j-1)+t) ) );
CB(n, k)=if (n==1,k, 1/(n*eulerphi(n)) * sum(t=0,n-1, sum(j=1,n-1, if(1==gcd(n,j), k^c(j,t,n), 0) ) ) );
for(n=1, 66, print1(CB(n,5),", "));
\\ Joerg Arndt, Aug 27 2014
A056374
Number of step shifted (decimated) sequences using a maximum of five different symbols.
Original entry on oeis.org
5, 25, 75, 375, 825, 8125, 13175, 103125, 327125, 2445625, 4884435, 61640625, 101732425, 1017323125, 3816215625, 19104609375, 47683838325, 635787765625, 1059638680675, 11924780390625, 39736963221875, 238418603522125, 541860418146375
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
-
a[m_, n_] := (1/EulerPhi[n])*Sum[If[GCD[k, n] == 1, m^DivisorSum[n, EulerPhi[#]/MultiplicativeOrder[k, #] &], 0], {k, 1, n}]; Table[a[5, n], {n, 1, 23}] (* Jean-François Alcover, Dec 04 2015 *)
A056414
Number of step cyclic shifted sequences using a maximum of six different symbols.
Original entry on oeis.org
6, 21, 56, 231, 462, 4291, 6966, 57561, 188866, 1519035, 3302922, 45921281, 83747286, 933081411, 3920355712, 22075451286, 62230996506, 940379310731, 1781757016326, 22856965214727, 87052415641136, 598280600648031, 1560731765058606, 24680195365765751, 56860576713326910, 546736312124316741, 2105947271634851386
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
-
M[j_, L_] := Module[{m = 1}, While[Sum[ j^i, {i, 0, m - 1}] ~Mod~ L != 0, m++]; m]; c[j_, t_, n_] := Sum[ 1/M[j, n / GCD[n, u*(j - 1) + t] ], {u, 0, n - 1}]; CB[n_, k_] = If[n == 1, k, 1/(n*EulerPhi[n]) * Sum[ If[1 == GCD[n, j], k^c[j, t, n], 0], {t, 0, n-1}, {j, 1, n-1}]]; Table[ Print[ cb = CB[n, 6]]; cb, {n, 1, 27}] (* Jean-François Alcover, Dec 04 2015, after Joerg Arndt *)
-
\\ see p.3 of the Dokovic et al. reference
M(j, L)={my(m=1); while ( sum(i=0, m-1, j^i) % L != 0, m+=1 ); m; }
c(j, t, n)=sum(u=0,n-1, 1/M(j, n / gcd(n, u*(j-1)+t) ) );
CB(n, k)=if (n==1,k, 1/(n*eulerphi(n)) * sum(t=0,n-1, sum(j=1,n-1, if(1==gcd(n,j), k^c(j,t,n), 0) ) ) );
for(n=1, 66, print1(CB(n,6),", "));
\\ Joerg Arndt, Aug 27 2014
A056376
Number of step shifted (decimated) sequences using exactly two different symbols.
Original entry on oeis.org
0, 2, 4, 10, 10, 38, 26, 94, 102, 278, 214, 1246, 702, 2798, 4342, 8926, 8230, 44222, 29202, 136030, 176750, 419870, 381490, 2150398, 1678254, 5593998, 7461166, 22553406, 19175158, 134391038, 71585134
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A056392
Number of step shifted (decimated) sequence structures using a maximum of three different symbols.
Original entry on oeis.org
1, 2, 4, 10, 14, 70, 68, 332, 577, 2510, 2980, 23372, 22218, 133150, 300964, 909382, 1345634, 10767202, 10762820, 72957100, 145362932, 523029526, 713213956, 5893709440, 7060765733, 35303782550
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A056393
Number of step shifted (decimated) sequence structures using a maximum of four different symbols.
Original entry on oeis.org
1, 2, 4, 11, 17, 107, 131, 811, 1893, 11107, 17599, 179371, 233449, 1866057, 5603787, 22469291, 44744047, 477262537, 636308685, 5732457131, 15272176697, 73301054891, 133274359129, 1466413263531
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A056394
Number of step shifted (decimated) sequence structures using a maximum of five different symbols.
Original entry on oeis.org
1, 2, 4, 11, 18, 116, 157, 1110, 3076, 21808, 42335, 528612, 859502, 8547036, 31968397, 159716545, 398048506, 5303680564, 8835749347, 99411986634, 331215914028, 1987084129352, 4515860983385, 62095481040014
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A056429
Number of step cyclic shifted sequence structures using a maximum of two different symbols.
Original entry on oeis.org
1, 2, 2, 4, 3, 8, 5, 14, 11, 26, 15, 88, 37, 130, 184, 357, 261, 1346, 805, 3760, 4434, 9758, 8385, 47462, 33781, 108330, 138767, 408376, 331185, 2251816, 1155735
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A056430
Number of step cyclic shifted sequence structures using a maximum of three different symbols.
Original entry on oeis.org
1, 2, 3, 6, 6, 22, 16, 66, 83, 300, 296, 2243, 1778, 9780, 20640, 58428, 79554, 600798, 567544, 3671978, 6935746, 23785912, 31017008, 246156513, 282456333, 1357927400, 2615206733, 11358512518
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
A056431
Number of step cyclic shifted sequence structures using a maximum of four different symbols.
Original entry on oeis.org
1, 2, 3, 7, 7, 33, 29, 149, 245, 1230, 1665, 15973, 18199, 134482, 376433, 1415209, 2634597, 26534612, 33499359, 287002711, 727425501, 3332040944, 5794658931, 61120855045, 93825569009, 601444738252
Offset: 1
- M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
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