Original entry on oeis.org
1, 3, 13, 105, 1681, 53793, 3442753, 440672385, 112812130561
Offset: 0
A076131
a(n) = 2^n*a(n-1) + 1, a(0) = 0.
Original entry on oeis.org
0, 1, 5, 41, 657, 21025, 1345601, 172236929, 44092653825, 22575438758401, 23117249288602625, 47344126543058176001, 193921542320366288900097, 1588605274688440638669594625, 26027708820495411423962638336001, 852875962629993641540407732994080769
Offset: 0
Kyle Hunter (hunterk(AT)raytheon.com), Oct 31 2002
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a[0] = 0; a[n_] := 2^n a[n - 1] + 1; Table[ a[n], {n, 0, 13}]
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a(n)=if(n<0,0,subst(Polrev(Vec(sum(k=1,n,x^(k*(k+1)/2)))),x,2))
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a(n)=if(n<1,0,1+a(n-1)*2^n)
Original entry on oeis.org
1, 2, 5, 21, 169, 2705, 86561, 5539905, 709107841, 181531607297, 92944182936065, 95174843326530561, 194918079132734588929, 798384452127680876253185, 6540365431829961738266091521, 107157347235102093119751643480065, 3511331954199825387348021853554769921
Offset: 0
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Table[Sum[2^((n(n-1))/2-(k(k-1))/2),{k,0,n}],{n,0,20}] (* Harvey P. Dale, Jul 05 2023 *)
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a(n)=sum(k=0,n,2^((n-k)*(n+k-1)/2))
A225609
Recurrence a(n) = 2^n*a(n-1) + a(n-2) with a(0)=0, a(1)=1.
Original entry on oeis.org
0, 1, 4, 33, 532, 17057, 1092180, 139816097, 35794013012, 18326674478241, 18766550459731796, 38433913668205196449, 157425329151518944386900, 1289628334843156860622681249, 21129270795495611155960953970516, 692363946716428521201685400328549537
Offset: 0
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RecurrenceTable[{a[n]==2^n*a[n-1]+a[n-2],a[0]==0,a[1]==1},a,{n,0,15}]
A228467
Recurrence a(n) = 2^n*a(n-1) - a(n-2) with a(0)=0, a(1)=1.
Original entry on oeis.org
0, 1, 4, 31, 492, 15713, 1005140, 128642207, 32931399852, 16860748082017, 17265373104585556, 35359467257443136671, 144832360621113983218860, 1186466662848698493085764449, 19439069659280715489603181513556, 636979433408843822314618558750438559
Offset: 0
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RecurrenceTable[{a[n]==2^n*a[n-1]-a[n-2],a[0]==0,a[1]==1},a,{n,0,15}]
nxt[{n_,a_,b_}]:={n+1,b,b*2^(n+1)-a}; NestList[nxt,{1,0,1},20][[All,2]] (* Harvey P. Dale, Jul 02 2022 *)
A371441
a(n) = a(n-1)*3^n + 1 where a(0)=1.
Original entry on oeis.org
1, 4, 37, 1000, 81001, 19683244, 14349084877, 31381448626000, 205893684435186001, 4052605390737766057684, 239302295717674347940182517, 42391683779498857714559512339000, 22528678819460652442683221796950499001, 35917990801478965784376042224979510418771324
Offset: 0
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Table[Sum[3^(k*(2*n + 1 - k)/2), {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Apr 10 2024 *)
Block[{n = 0}, NestList[#*3^++n + 1 &, 1, 15]] (* Paolo Xausa, Apr 19 2024 *)
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l = [1]
for i in range(1,14):
l.append(l[-1]*pow(3,i) + 1)
print(l)
Showing 1-6 of 6 results.
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